Geometric Routing in Sensor Networks III: Geometric Routing in - PowerPoint PPT Presentation

Geometric Routing in Sensor Networks III: Geometric Routing in Sensor Networks III: Explore the Global Topology Explore the Global Topology Jie Gao Computer Science Department Stony Brook University 10/5/06 Jie Gao, CSE590-fall06 1

Routing around holes Routing around holes • Real-world deployment is not uniform, has holes (due to buildings, landscape variation). • Face routing is too “Short-sighted” and greedy. • Boundary nodes get overloaded. 10/5/06 Jie Gao, CSE590-fall06 2

Intuition Intuition • When sensors are densely uniformly deployed, greedy forwarding is sufficient most of the time. • When the sensor field is irregular (holes become prominent), capture this topological information for routing. • What is wrong with greedy routing with holes? Mismatch between routing rule & network connectivity. 10/5/06 Jie Gao, CSE590-fall06 3

Routing around holes Routing around holes Two ways to get around the hole Routing rule Face routing: short-sighted 10/5/06 Jie Gao, CSE590-fall06 4

Topology is important Topology is important • The global topology of the sensor field: – # holes (genus). – Positions of holes. • Three questions: – How to extract it? – How to represent it? – How to use it? 10/5/06 Jie Gao, CSE590-fall06 5

General methodology General methodology • 2-level infrastructure • Top-level: capture the global topology. – Where the holes are (e.g., CS building, Javitz center, etc). – General routing guidance (e.g., get around the Javitz center, go straight to SAC). • Bottom-level: capture the local connectivity. – Gradient descent to realize the routing path. 10/5/06 Jie Gao, CSE590-fall06 6

2- -level infrastructure level infrastructure 2 • Why this makes sense? – Global topology is stable (the position of buildings are unlikely to change often). – Global topology is compact (a small number of buildings) • From each node’s point of view: – A rough guidance. – Local greedy rule. 10/5/06 Jie Gao, CSE590-fall06 7

Papers Papers • Qing Fang, Jie Gao, Leonidas Guibas, Vin de Silva, Li Zhang, GLIDER: Gradient Landmark-Based Distributed Routing for Sensor Networks , Proc. of the 24th Conference of the IEEE Communication Society (INFOCOM'05), March, 2005. • J. Bruck, J. Gao, A. Jiang, MAP: Medial Axis Based Geometric Routing in Sensor Networks , to appear in the 11th Annual International Conference on Mobile Computing and Networking (MobiCom’05), August, 2005. Major difference: different ways to capture the global topology. 10/5/06 Jie Gao, CSE590-fall06 8

GLIDER: Landmark- -based schemes based schemes GLIDER: Landmark • We use landmarks in real life: – 5 th ave and 42 street. – Two blocks after bank of America. • Use landmark-based virtual coordinates. 10/5/06 Jie Gao, CSE590-fall06 9

Combinatorial Delaunay graph Combinatorial Delaunay graph • Given a communication graph on sensor nodes, with path length in shortest path hop counts • Select a set of landmarks • Landmarks flood the network. Each node learns the hop count to each landmark. • Construct Landmark Voronoi Complex (LVC) 10/5/06 Jie Gao, CSE590-fall06 10

Combinatorial Delaunay graph Combinatorial Delaunay graph • Construct Landmark Voronoi Complex (LVC) • Each sensor identifies its closest landmark. • A sensor is on the boundary if it has 2 closest landmarks. • If flooding are synchronized, then restricted flooding up to the boundary nodes is enough. 10/5/06 Jie Gao, CSE590-fall06 11

Combinatorial Delaunay graph Combinatorial Delaunay graph • Construct Combinatorial Delaunay Triangulation (CDT) on landmarks • If there is at least one boundary node between landmark i and j, then there is an edge ij in CDT. • Holes in the sensor field map to holes in CDT. • CDT is broadcast to the whole network. 10/5/06 Jie Gao, CSE590-fall06 12

Virtual coordinates Virtual coordinates Each node stores virtual coordinates (d 1 , d 2 , d 3 , … d k ), d k = hop count to the kth reference landmark (home+neighboring landmarks) home landmark (think about post-office) resident tile p reference landmarks Boundary nodes 10/5/06 Jie Gao, CSE590-fall06 13

Combinatorial Delaunay graph Combinatorial Delaunay graph Theorem : If G is connected, then the Combinatorial Delaunay graph D(L) for any subset of landmarks is also connected. 1. Compact and stable 2. Abstract the connectivity graph: Each edge can be mapped to a path that uses only the nodes in the two corresponding Voronoi tiles; Each path in G can be “lifted” to a path in D(L) 10/5/06 Jie Gao, CSE590-fall06 14

Information Stored at Each Node Information Stored at Each Node • The shortest path tree on D(L) rooted at its home landmark • Its coordinates and those of its neighbors for greedy routing 10/5/06 Jie Gao, CSE590-fall06 15

Virtual coordinates Virtual coordinates • With the virtual coordinates, a node can test if – It is on the boundary (two closest landmarks). – A neighbor who is closer to a reference landmark. 10/5/06 Jie Gao, CSE590-fall06 16

Local Routing with Global Guidance Local Routing with Global Guidance • Global Guidance: routing on tiles the D(L) that encodes global connectivity information is accessible to every node for proactive route planning on tiles. • Local Routing: how to go from tile to tile. high-level routes on tiles are realized as actual paths in the network by using reactive protocols. 10/5/06 Jie Gao, CSE590-fall06 17

GLIDER -- -- Routing Routing GLIDER 1. Global planning u 3 u u u 3 3 3 u 2 u u u 2. Local routing 2 2 2 q q q q u u u 1 u – Inter-tile routing 1 1 1 p p p p – Intra-tile routing 10/5/06 Jie Gao, CSE590-fall06 18

Intra- -tile routing tile routing Intra • How to route from one node to L 5 L 1 the other inside a tile? • Each node knows the hop count to home landmark and p q neighboring landmarks. L 0 • No idea where the landmarks are. L 4 L 2 • A bogus proposal: p routes to L 3 the home landmark then routes to q. 10/5/06 Jie Gao, CSE590-fall06 19

Centered Landmark- -Distance Coordinates and Distance Coordinates and Centered Landmark Greedy Routing Greedy Routing L 5 L 1 Reference landmarks: L 0 ,…L k T(p) = L 0 2 ,…, pL k 2 ) Let s = mean(pL 0 p q Local virtual coordinates: L 0 2 – s,…, pL k 2 – s) c(p)= (pL 0 L 4 (centered metric) L 2 Distance function: L 3 2 d(p, q) = |c(p) – c(q)| Greedy strategy : to reach q, do gradient descent on the function d(p, q) 10/5/06 Jie Gao, CSE590-fall06 20

Local Landmark Coordinates – – No Local Minimum No Local Minimum Local Landmark Coordinates • Theorem : In the continuous Euclidean plane, gradient descent on the function d(p, q) always converges to the destination q, for at least three non-collinear landmarks. • Landmark-distance coordinates Landmark i • Centered coordinates • The function is a linear function! 10/5/06 Jie Gao, CSE590-fall06 21

Node Density vs. Success Rate of Greedy Routing Node Density vs. Success Rate of Greedy Routing In the discrete case, we empirically observe that landmark gradient descending does not get stuck on networks with reasonable density (each node has on average six neighbors or more). 2000 nodes distributed on a perturbed grid. Perturbation ~ Gaussian(0, 0.5r), where r is the radio range 10/5/06 Jie Gao, CSE590-fall06 22

u u 3 u u 3 3 3 u u 2 u u 2 2 2 q q q q u 1 u u u 1 1 1 p p p p 10/5/06 Jie Gao, CSE590-fall06 23

Examples Examples Each node on average has 6 one-hop neighbors. 10/5/06 Jie Gao, CSE590-fall06 24

Simulations – – Path Length and Load Balancing Path Length and Load Balancing Simulations GLIDER 41 hops GPSR 52 hops Each node on average has 6 one-hop neighbors. 10/5/06 Jie Gao, CSE590-fall06 25

Simulations – – Hot Spots Comparison Hot Spots Comparison Simulations Randomly pick 45 source and destination pairs, each separated by more than 30 hops. GLIDER GPSR Blue (6-8 transit paths), orange (9-11 transit paths), black (>11 transit paths) 10/5/06 Jie Gao, CSE590-fall06 26

Stability Stability • Landmark failure. – Not a big problem as the landmark is simply a point of reference. – Not like gateway. • Combinatorial Delaunay edge change? – Requires big change in the network topology (merge of holes, disconnect a band of nodes, etc). 10/5/06 Jie Gao, CSE590-fall06 27

Open issues in GLIDER Open issues in GLIDER • How to select landmarks? What is a good criterion in selecting landmarks? • What can we say about the intra-tile greedy routing on a discrete network? • one of the challenges is that the hop count is a rough estimation of the Euclidean distance. 10/5/06 Jie Gao, CSE590-fall06 28

Beacon Vector Routing (BVR) Beacon Vector Routing (BVR) • Another heuristic landmark-based routing. • Every node remembers hop counts to a total of r landmarks. • Routing metric: – Pulling landmarks (those closer to destination). Dist from d to landmark i. Dist from p to landmark i. – Pushing landmarks (further to destination) 10/5/06 Jie Gao, CSE590-fall06 29